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PreprintCC BY 4.0arXiv

Counterexample to a Proposed Capacity Characterization of the Relay Channel

  • Chun Hei Michael Shiu
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Abstract

We present a counterexample to the relay channel capacity characterization proposed in a recent work, which is based on properties of typical sequences. The counterexample uses a binary relay channel with a noiseless source-destination component and binary symmetric relay links. An achievable scheme exceeds the proposed capacity characterization, thereby disproving the characterization of the capacity for general relay channels. We highlight that the counterexample is obtained with the assistance of ChatGPT-6 Astra and the proofs are simplified with human effort.

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Cite

BibTeXRIS
BibTeX
@misc{shiu2026counterexample,
  title = {{Counterexample to a Proposed Capacity Characterization of the Relay Channel}},
  author = {Chun Hei Michael Shiu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18727},
  eprint = {2609.18727},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18727},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Counterexample to a Proposed Capacity Characterization of the Relay Channel
AU  - Chun Hei Michael Shiu
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18727
UR  - https://arxiv.org/abs/2609.18727
AB  - We present a counterexample to the relay channel capacity characterization proposed in a recent work, which is based on properties of typical sequences. The counterexample uses a binary relay channel with a noiseless source-destination component and binary symmetric relay links. An achievable scheme exceeds the proposed capacity characterization, thereby disproving the characterization of the capacity for general relay channels. We highlight that the counterexample is obtained with the assistance of ChatGPT-6 Astra and the proofs are simplified with human effort.
ER  -